đấy nhá

b) Ta có: \(\left|x\right|-\dfrac{3}{4}=\dfrac{5}{3}\)

\(\Leftrightarrow\left|x\right|=\dfrac{5}{3}+\dfrac{3}{4}=\dfrac{20}{12}+\dfrac{9}{12}=\dfrac{29}{12}\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{29}{12}\\x=-\dfrac{29}{12}\end{matrix}\right.\)

c) Ta có: \(\left|2x-\dfrac{1}{3}\right|+\dfrac{5}{6}=1\)

\(\Leftrightarrow\left|2x-\dfrac{1}{3}\right|=\dfrac{1}{6}\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-\dfrac{1}{3}=\dfrac{1}{6}\\2x-\dfrac{1}{3}=\dfrac{-1}{6}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=\dfrac{1}{6}+\dfrac{1}{3}=\dfrac{1}{2}\\2x=\dfrac{1}{6}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{4}\\x=\dfrac{1}{12}\end{matrix}\right.\)

\(a) \sqrt{4x^2− 9} = 2\sqrt{x + 3}\)

\(ĐK:x\ge\dfrac{3}{2}\)

\(pt\Leftrightarrow4x^2-9=4\left(x+3\right)\)

\(\Leftrightarrow4x^2-9=4x+12\)

\(\Leftrightarrow4x^2-4x-21=0\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1-\sqrt{22}}{2}\left(l\right)\\x=\dfrac{1+\sqrt{22}}{2}\left(tm\right)\end{matrix}\right.\)

\(b)\sqrt{4x-20}+3.\sqrt{\dfrac{x-5}{9}}-\dfrac{1}{3}\sqrt{9x-45}=4\)

\(ĐK:x\ge5\)

\(pt\Leftrightarrow2\sqrt{x-5}+\sqrt{x-5}-\sqrt{x-5}=4\)

\(\Leftrightarrow2\sqrt{x-5}=4\Leftrightarrow\sqrt{x-5}=2\)

\(\Leftrightarrow x-5=4\Leftrightarrow x=9\left(tm\right)\)

\(c)\dfrac{2}{3}\sqrt{9x-9}-\dfrac{1}{4}\sqrt{16x-16}+27.\sqrt{\dfrac{x-1}{81}}=4\)

ĐK:x>=1

\(pt\Leftrightarrow2\sqrt{x-1}-\sqrt{x-1}+3\sqrt{x-1}=4\)

\(\Leftrightarrow4\sqrt{x-1}=4\Leftrightarrow\sqrt{x-1}=1\)

\(\Leftrightarrow x-1=1\Leftrightarrow x=2\left(tm\right)\)

\(d)5\sqrt{\dfrac{9x-27}{25}}-7\sqrt{\dfrac{4x-12}{9}}-7\sqrt{x^2-9}+18\sqrt{\dfrac{9x^2-81}{81}}=0\)

\(ĐK:x\ge3\)

\(pt\Leftrightarrow3\sqrt{x-3}-\dfrac{14}{3}\sqrt{x-3}-7\sqrt{x^2-9}+6\sqrt{x^2-9}=0\)

\(\Leftrightarrow-\dfrac{5}{3}\sqrt{x-3}-\sqrt{x^2-9}=0\Leftrightarrow\dfrac{5}{3}\sqrt{x-3}+\sqrt{x^2-9}=0\)

\(\Leftrightarrow(\dfrac{5}{3}+\sqrt{x+3})\sqrt{x-3}=0\)

\(\Leftrightarrow\sqrt{x-3}=0\)    (vì \(\dfrac{5}{3}+\sqrt{x+3}>0\))

\(\Leftrightarrow x-3=0\Leftrightarrow x=3\left(nhận\right)\)

a.

\(\dfrac{x}{9}=\dfrac{4}{x}\)

\(\Rightarrow x^2=4.9\)

\(\Rightarrow x^2=36\)

\(\Rightarrow\left[{}\begin{matrix}x=-6\\x=6\end{matrix}\right.\)

b.

\(\dfrac{x+1}{3}=\dfrac{3}{x+1}\)

\(\Rightarrow\left(x+1\right)^2=3^2\)

\(\Rightarrow\left[{}\begin{matrix}x+1=3\\x+1=-3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=2\\x=-4\end{matrix}\right.\)

\(\dfrac{x}{9}=\dfrac{4}{x}\)

\(x^2=4.9\)

\(x^2=36\)

\(x^2=6^2\)

\(\Rightarrow\left\{{}\begin{matrix}x=6\\x=-6\end{matrix}\right.\)

\(---------\)

\(\dfrac{x+1}{3}=\dfrac{3}{x+1}\)

\(\left(x+1\right)^2=3.3=3^2\)

\(\Rightarrow\left(1\right):x+1=3\)

            \(x=3-1\Rightarrow x=2.\)

\(\Rightarrow\left(2\right):x+1=-3\)

             \(x=-3-1\Rightarrow x=-4\)

Từ \(\left(1\right)\) và \(\left(2\right)\), ta suy ra:

\(\Rightarrow x\in\left\{{}\begin{matrix}2\\-4\end{matrix}\right.\)

a, \(\dfrac{6}{x-3}=\dfrac{9}{2x-7}\)

=> 6(2x-7) = 9(x-3)

=> 12x - 42 = 9x - 27

=> 12x - 9x = -27 + 42

=> 3x = 15 

=> x = 5

Vậy x = 5

b, \(\dfrac{-7}{x+1}=\dfrac{6}{x+27}\)

=> -7(x + 27) = 6(x + 1)

=> -7x - 189 = 6x + 6

=> -7x - 6x = 6 + 189

=> -13x = 195

=> x = -15

Vậy x = -15

a) Ta có: \(\dfrac{6}{x-3}=\dfrac{9}{2x-7}\)

\(\Leftrightarrow6\left(2x-7\right)=9\left(x-3\right)\)

\(\Leftrightarrow12x-42=9x-27\)

\(\Leftrightarrow12x-9x=-27+42\)

\(\Leftrightarrow3x=15\)

hay x=5

Vậy: x=5

b) Ta có: \(\dfrac{-7}{x+1}=\dfrac{6}{x+27}\)

\(\Leftrightarrow6\left(x+1\right)=-7\left(x+27\right)\)

\(\Leftrightarrow6x+6=-7x+189\)

\(\Leftrightarrow6x+7x=189-6\)

\(\Leftrightarrow13x=183\)

hay \(x=\dfrac{183}{13}\)

Vậy: \(x=\dfrac{183}{13}\)

\(C=\left(\dfrac{x-3\sqrt{x}-x-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\right)\cdot\dfrac{\sqrt{x}-3}{2\sqrt{x}+4}\)

\(=\dfrac{-3}{2\sqrt{x}+4}\)

Để \(C< -\dfrac{1}{3}\) thì \(\dfrac{-3}{2\sqrt{x}+4}+\dfrac{1}{3}< 0\)

\(\Leftrightarrow-9+2\sqrt{x}+4< 0\)

\(\Leftrightarrow\sqrt{x}< \dfrac{5}{2}\)

hay \(0\le x< \dfrac{25}{4}\)

a: \(B=\dfrac{\sqrt{x}}{\sqrt{x}+3}-\dfrac{x+9}{x-9}\)

\(=\dfrac{x-3\sqrt{x}-x-9}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)

\(=\dfrac{-3}{\sqrt{x}-3}\)

\(x+\dfrac{40}{27}=2\)
\(x=\dfrac{14}{27}\)

\(x+1+\dfrac{1}{3}+\dfrac{1}{9}+\dfrac{1}{27}+\dfrac{1}{81}=2\)

\(\Leftrightarrow x+\dfrac{121}{81}=2\)

hay \(x=\dfrac{41}{81}\)

a: Ta có: \(A=\dfrac{2x}{x+3}+\dfrac{x+1}{x-3}+\dfrac{3-11x}{9-x^2}\)

\(=\dfrac{2x^2-6x+x^2+4x+3-3+11x}{\left(x+3\right)\left(x-3\right)}\)

\(=\dfrac{3x^2+9x}{\left(x+3\right)\left(x-3\right)}\)

\(=\dfrac{3x}{x-3}\)

b: Ta có P=AB

nên \(P=\dfrac{3x}{x-3}\cdot\dfrac{x-3}{x+1}=\dfrac{3x}{x+1}\)

Để \(P=\dfrac{9}{2}\) thì 9x+9=6x

\(\Leftrightarrow3x=-9\)

hay x=-3(loại)

a) \(A=\dfrac{2x}{x+3}+\dfrac{x+1}{x-3}+\dfrac{3-11x}{9-x^2}\\ \Rightarrow A=\dfrac{2x}{x+3}+\dfrac{x+1}{x-3}-\dfrac{3-11x}{\left(x-3\right)\left(x+3\right)}\)

    \(\Rightarrow A=\dfrac{2x\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}+\dfrac{\left(x+1\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\dfrac{3-11x}{\left(x-3\right)\left(x+3\right)}\)

    \(\Rightarrow A=\dfrac{2x\left(x-3\right)+\left(x+1\right)\left(x+3\right)-3+11x}{\left(x-3\right)\left(x+3\right)}\)

    \(\Rightarrow A=\dfrac{2x^2-6x+x^2+4x+3-3+11x}{\left(x-3\right)\left(x+3\right)}\)

    \(\Rightarrow A=\dfrac{3x^2+9x}{\left(x-3\right)\left(x+3\right)}\)

    \(\Rightarrow A=\dfrac{3x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}\)

    \(\Rightarrow A=\dfrac{3x}{x-3}\)

a. ĐKXĐ: \(x\ne\pm3\)

\(A=\dfrac{2x}{x+3}+\dfrac{x+1}{x-3}+\dfrac{3-11x}{9-x^2}\)

\(=\dfrac{2x}{x+3}+\dfrac{x+1}{x-3}-\dfrac{3-11x}{x^2-9}\)

\(=\dfrac{2x\left(x-3\right)+\left(x+1\right)\left(x+3\right)-\left(3-11x\right)}{x^2-9}\)

\(=\dfrac{2x^2-6x+x^2+4x+3-3+11x}{x^2-9}\)

\(=\dfrac{3x^2+9x}{x^2-9}=\dfrac{3x\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}=\dfrac{3x}{x-3}\)

b. \(P=A.B\)

\(\Rightarrow P=\dfrac{3x}{x-3}.\dfrac{x-3}{x+1}=\dfrac{3x}{x+1}\) 

Ta có \(P=\dfrac{9}{2}\) 

\(\Leftrightarrow\left\{{}\begin{matrix}x\ne-1\\\dfrac{3x}{x+1}=\dfrac{9}{2}\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ne-1\\6x=9x+9\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ne-1\\-3x=9\end{matrix}\right.\) \(\Leftrightarrow x=-3\)

c. \(B< 1\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ne-1\\\dfrac{x-3}{x-1}< 1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ne-1\\\dfrac{x-3}{x-1}-1< 0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ne-1\\\dfrac{2}{1-x}< 0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ne-1\\1-x< 0\end{matrix}\right.\) \(\Leftrightarrow x>1\)